(1) Field of the Invention
The present invention relates to circular synthetic aperture sonar. More particularly, the present invention relates to a method of focusing fully-coherent circular synthetic aperture imagery without the aid of a navigation beacon.
(2) Description of the Prior Art
Circular synthetic aperture sonar (CSAS) is a specific modality of synthetic aperture sonar in which individual pings from a sonar device having a circular trajectory are coherently processed to generate an image having a full 360° of backscattered aspect information. In contrast, “linear-scan” synthetic aperture sonar coherently processes backscattered echoes from a narrow range of aspects, typically in the low tens of degrees, to generate an image.
Circular synthetic aperture sonar images are useful because of the large amount of information recovered for a particular scene, and echoes backscattered from all aspects can be used to generate target outlines and high resolution imagery. While theoretically very useful, focused CSAS images are difficult to obtain due to motion constraints. A major source of defocusing in CSAS imagery are deviations of the sonar platform from a circular trajectory, such as caused by wave action, path tracking errors and the like.
As noted, a CSAS image is an image generated using the entire set of backscattered echoes gathered from a platform moving around a circular aperture. Sub-aperture (SA) images, which are distinct from CSAS images, can be generated using any limited portion of the circular aperture (e.g., an image can be made using the set of look angles spanning from 30° to 50°). Sway error, which is unique for individual sub-apertures, tends to cause the scene to shift as a function of look-angle.
One auto-focus method known in the art works by generating multiple SA intensity images, typically numbering in the low tens. The algorithm attempts to optimally shift and sum these images to counteract for the scene shift caused by platform motion. To do this, each of these SA images is correlated with the others, an operation requiring N*(N−1)/2 image correlations.
The relative locations of the correlation peaks in the X and Y coordinates of the sub-aperture image and the signal-to-noise values gathered from the correlation peaks are used to generate a robust least-squares polynomial expression for the scene shift. The resulting polynomial is used to estimate the optimal scene shift that can be applied to each sub-aperture to align them all before summing.
While the algorithm appears to be fairly robust, there are two major drawbacks to this method. First, it is a non-iterative algorithm that provides no motion solution. The relationship between the scene shift and the actual platform motion in a CSAS scenario is essential for making a navigational correction which could potentially result in a fully-coherent, high-resolution CSAS image. However, the relationship is not obvious and has not been outlined in the literature.
The second drawback to the multiple SA method is that the order of the polynomial expression is often much too small to accurately model the platform motion. A fundamental assumption in the outlined algorithm is that the motion error within any of the sub-apertures can be approximated as negligible.
Because of the large number or correlations that must occur relative to the actual number of apertures utilized, (N*(N−1)/2, N=number of sub-apertures), and the tendency for coefficients of the polynomial solution to quickly exceed machine precision, the number of sub-apertures remains limited in order. One published example of the multiple SA method uses thirty (N=30) sub-apertures (H. J. Callow, R. E. Hanson, S. Synnes, and T. O. Saebo, “Circular synthetic aperture sonar without a beacon,” Proceedings of the 3rd International Conference & Exhibition on Underwater Acoustic Measurements, June 2009). For many synthetic aperture sonar parameters and environments, this limited number of sub-apertures remains insufficient to accurately model platform motion.
A second auto-focus method known in the art uses a maximum a-posteriori (MAP) estimator to attempt to simultaneously focus a CSAS image and determine scene bathymetry, decoupling scene elevation from platform motion (H. J. Callow, S. Synnes, T. O. Saebo, R. E. Hanson “Autofocus for circular synthetic aperture imaging,” Proceedings of Synthetic Aperture Sonar and Synthetic Aperture Radar (SAS/SAR) 2010, Lerici, Italy, September 2010). While the concepts in this approach are directly applicable to CSAS, the data sets used in the published example of this method were obtained from four looks along the cardinal directions at the same scene using four independent line-scans rather than a circular path trajectory.
As described in the literature, the approach offers no method for recovering a platform motion estimate. Accordingly, the efficacy of this approach in the context of an actual CSAS scenario, in which a platform undergoes rapid motion error, remains to be demonstrated.
Methods used in circular synthetic aperture radar (CSAR) may be adapted to CSAS. While most examples of CSAR use error-free data recorded from a fixed source and rotating platform, there are known in the art examples of CSAR imagery recorded from an aircraft rather than a fixed system. Some of these examples mention Phase Gradient Autofocus/Phase Curvature Autofocus based focusing methods.
The draw-back of these methods is that they require prominent points with uniform angular response. In the examples known in the art, the prominent points were provided by artificially placing bright, point-like targets in the scene before imaging took place. These methods also assume a-priori that the blurring of the targets is small enough that they remain distinct from adjacent scatterers. Such assumptions do not hold well in many CSAS imaging scenarios.
Another auto-focus method pertaining to CSAR is a correlation based map-drift algorithm similar to the multiple SA method described previously. This CSAR method operates by forming a large number of small apertures. The image shifts are found by correlating each sub-aperture with the accumulated sum of the aligned versions of all previous apertures, starting with the first look angle.
This saves considerable time from a correlation standpoint. However, to calculate the associated trajectory, a set of linear equations relating each apparent location to all other locations is established and singular-value-decomposition (SVD) is used to solve for the navigation correction. This method applies the navigation correction to the raw data which is then re-beamformed. The algorithm used in the method can be iterated.
While this method has a speed advantage with respect to the multiple SA method described previously, the navigation solution must be applied to the raw data, requiring multiple iterated instances of beamforming, reducing computational efficiency. Furthermore, this method of sub-aperture scene tracking lacks a direct measurement of phase curvature error, resulting in sub-optimal precision for high frequency error estimation.
Thus, a need has been recognized in the state of the art to provide a method of focusing fully-coherent circular synthetic aperture imagery without the aid of a navigation beacon. The method needs to be iterative in order to accurately model platform motion. The method should be applicable without the need to use prominent points within the field that have uniform angular response. Further, the method should be computationally efficient without requiring re-beamforming.